I agree with goofyernmost. For the OP, what would you leave in the room so that you can use this case and avoid bag check?
And a more pertinent question, why? If you want the extra shoes, if nothing else, just spend the extra 1-3 minutes to go through bag check. It's just not that big a deal.
I DO bring a backpack, but that is because I visit in my role as a group tour director. I need my binder of information and several other items for my group. And as the PP said, as long as you try to pick a short(er) line and have your compartments open, it takes just a few seconds. I joke with the guard about being the group pack mule, we share a laugh, and I'm headed in the park.